CTET and State TET Maths – LCM and HCF Concepts

LCM stands for Lowest Common Multiple, and HCF stands for Highest Common Factor.

The key to telling the difference between these two things is knowing the difference between a multiple and a factor.

A multiple of an integer (whole number) is any integer that appears in its times table. For example, the multiples of 3 are 3, 6, 9, 12, and so on.

A factor of an integer is any integer that divides the integer with no remainder. For example, the factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36.

We use LCM and HCF to compare two (or more) integers.

The following diagram shows how to find the HCF and LCM of 24 and 36 using Repeated Division.

Almost every CTET question paper has questions on LCM and HCF.

Previous Year Questions:

Question #1 LCM of two prime numbers x and y, (x > y), is 161. The value of 3y – x is

[Mathematics] [CTET-2014-09]
Options
  • 2
  • -2 correct answer
  • -5
  • 62
Question #2 HCF of two numbers is 28 and their LCM is 336. If one number is 112, then the other number is

[Mathematics] [CTET-2013-07]
Options
  • 56
  • 70
  • 84 correct answer
  • 98
Answer Explanation Using the formula HCF X LCM = number1 x number2
=> 28×336 = 112 x number2
=> number2 = 28×336/112 = 28×3 = 84
Question #3 LCM of 22, 54, 135 and 198 is

[Mathematics] [CTET-2015-02]
Options
  • 22 x 33 x 5 x 11
  • 2 x 33 x 5 x 11 correct answer
  • 22 x 32 x 5 x 11
  • 23 x 32 x 5 x 11
Answer Explanation
2 22 54 135 198
3 11 27 135 99
3 11 9 45 11
3 11 3 15 11
5 11 1 5 11
11 11 1 1 11
1 1 1 1
Question #4 The HCF and LCM of two numbers are 12 and 72 respectively. If the sum of these numbers is 60,then one of the numbers will be

[Mathematics] [UPTET-2017-10]
Options
  • 12
  • 24 correct answer
  • 60
  • 72